Abstract

The problem of modeling and analyzing output processes of linear continuous stochastic systems is considered and the method for its solution based on the spectral form of mathematical description of the control systems is proposed. The proposed approach provides an explicit representation of the output signal of the system in the form of functional series with random coefficients or in the form of a partial sum in the approximate solution, which distinguishes this method from other approaches when the result of the solution are the deterministic characteristics of the output signal: the first two moments or the probability density function. As an application, the problem of modeling the action of wind is considered using the Dryden shaping filter.

中文翻译：

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基于随机函数正交展开的线性连续随机系统输出过程的建模与分析

摘要

考虑了线性连续随机系统的输出过程的建模和分析问题，提出了基于控制系统数学描述的谱形式的线性求解方法。所提出的方法以具有随机系数的函数序列的形式或近似解决方案中的部分和的形式提供系统输出信号的显式表示，当解决方案的结果为输出信号的确定性特征：前两个时刻或概率密度函数。作为应用，可以使用Dryden整形过滤器来考虑对风的行为进行建模的问题。